Comparison between observations of z ∼ 6 quasars and simulations. Left panel: the orange histogram shows the probability distribution function of Eddington ratios measured from the literature sample of quasars at 6 < z < 7.5. This is compared with Eddington ratio values obtained from the Eddington-limited accretion model (V21; blue histogram), and with Eddington ratio values obtained in post processing from V21 using Eq. (1) (green histogram). Right panel: distribution of the σ values obtained by applying the two-sample K–S test on N_{re − samp} = 10⁶ number of resamples. The blue (green) PDF refers to the σ distribution corresponding to the original (post-processed) values of λ_Edd from the V21 simulation. The vertical blue and green dashed lines show the median of the blue and green distributions, respectively.